## [1] "Run Completed at 2018-02-05 14:01:20"
\[ Yobs_{i,j} \sim Bernoulli(N(0,1.68)) \]
Note that this is a random probability of interaction on a per observation basis. This is different than a random link model. If we are interested in a binary network, a random interaction probability model will lead to a link probability of 1-(1/2)^n in n sampling events.
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 0
## Unobserved stochastic nodes: 2221
## Total graph size: 8212
##
## Initializing model
\[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 452
## Unobserved stochastic nodes: 1769
## Total graph size: 7842
##
## Initializing model
For hummingbird species i feeding on plant species j observed at time k and sampling event observed by transect
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j,k}) \] \[ logit(\lambda_{i,j,k}) = \alpha_i + \beta_{1,i} * Traitmatch_{i,j} \]
## sink("models/TraitMatch.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## logit(s[x])<-alpha[Bird[x]] + beta1[Bird[x]] * Traitmatch[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x]] + beta1[NewBird[x]] * Traitmatch[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i] ~ dnorm(alpha_mu,alpha_tau)
##
## #Traits slope
## beta1[i] ~ dnorm(beta1_mu,beta1_tau)
##
## }
##
## #Group process priors
##
## #Intercept
## alpha_mu ~ dnorm(0,0.386)
## alpha_tau ~ dt(0,1,1)I(0,)
## alpha_sigma<-pow(1/alpha_tau,0.5)
##
## #Trait
## beta1_mu~dnorm(0,0.386)
## beta1_tau ~ dt(0,1,1)I(0,)
## beta1_sigma<-pow(1/beta1_tau,0.5)
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 452
## Unobserved stochastic nodes: 813
## Total graph size: 8235
##
## Initializing model
To Do. Should I also do traits without the detection probabilities?
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect.jags")
## cat("
## model {
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Observation Process
## #True state
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## p[x]<-z[x] * s[x]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## pnew[x]<-znew[x]*snew[x]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
##
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 452
## Unobserved stochastic nodes: 3000
## Total graph size: 10303
##
## Initializing model
For hummingbird species i feeding on plant species j observed at time k and sampling event observed by transect
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j,k}) \] \[ logit(\lambda_{i,j,k}) = \alpha_i + \beta_{1,i} * Traitmatch_{i,j} \]
## sink("models/TraitMatch_Detect.jags")
## cat("
## model {
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Observation Process
## #True state
## z[x] ~ dbern(detect[Bird[x]])
##
## #observation
## logit(s[x])<-alpha[Bird[x]] + beta1[Bird[x]] * Traitmatch[Bird[x],Plant[x]]
## p[x]<-z[x] * s[x]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## logit(snew[x])<-alpha[NewBird[x]] + beta1[NewBird[x]] * Traitmatch[NewBird[x],NewPlant[x]]
## pnew[x]<-znew[x]*snew[x]
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
##
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i] ~ dnorm(alpha_mu,alpha_tau)
##
## #Traits slope
## beta1[i] ~ dnorm(beta1_mu,beta1_tau)
##
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #Group process priors
##
## #Intercept
## alpha_mu ~ dnorm(0,0.386)
## alpha_tau ~ dt(0,1,1)I(0,)
## alpha_sigma<-pow(1/alpha_tau,0.5)
##
## #Trait
## beta1_mu~dnorm(0,0.386)
## beta1_tau ~ dt(0,1,1)I(0,)
## beta1_sigma<-pow(1/beta1_tau,0.5)
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 452
## Unobserved stochastic nodes: 2044
## Total graph size: 10696
##
## Initializing model
Using the counts from the transects. Abundance is especially important to model, since its fluctuating all the time.
Do we have time for this?
If species co-occurrence is a prerequisite for interaction, then the absence of interactions may stem either from a lack of detectability or species absence. We can jointly model the presence of species as a function of elevation and then existance of an interaction.
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect_Elevation.jags")
## cat("
## model {
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Occurrence Process
## logit(psi[x])<-alpha_occ[Bird[x]] + beta_occ[Bird[x]] * elevation[x]
## occ[x] ~ dbern(psi[x])
##
## #Is the species available to be detected?
## rho[x]<-detect[Bird[x]]*occ[x]
##
## #Observation Process
## #True state
## z[x] ~ dbern(rho[x])
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## p[x]<-z[x] * s[x]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## #Occurrence Process
## logit(psi_new[x])<-alpha_occ[NewBird[x]] + beta_occ[NewBird[x]] * elevation_new[x]
## occ_new[x] ~ dbern(psi_new[x])
##
## #Is the species present to be detected?
## rho_new[x]<-detect[NewBird[x]]*occ_new[x]
## znew[x] ~ dbern(rho_new[x])
##
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## pnew[x]<-znew[x]*snew[x]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Note: flat logit priorsm - Following lunn 2012 p85
##
##
## #Occurrence Priors
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
##
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 452
## Unobserved stochastic nodes: 4261
## Total graph size: 16436
##
## Initializing model
Dashed line is the observed network from the time-series.
## # A tibble: 12 x 3
## # Groups: L1 [?]
## L1 value n
## <chr> <dbl> <dbl>
## 1 Random 0 41.3
## 2 Random 1.00 253
## 3 Species 0 55.2
## 4 Species 1.00 239
## 5 Species_Detect 0 216
## 6 Species_Detect 1.00 77.6
## 7 Species_Detect_Elevation 0 230
## 8 Species_Detect_Elevation 1.00 63.9
## 9 Traits 0 225
## 10 Traits 1.00 69.0
## 11 Traits_Detect 0 223
## 12 Traits_Detect 1.00 71.1
Dissimilairty in interactions (Beta_WN from Poisot 2012) Dashed line is the observed network from the time-series.
Create a kind of venn diagram on PCA of model similarity based on per link discrepency.
## # A tibble: 25 x 3
## # Groups: Model [6]
## Model mean pair
## <chr> <dbl> <chr>
## 1 Species_Detect_Elevation -1.00 Collared Inca_Bomarea multiflora
## 2 Species_Detect_Elevation -1.00 Collared Inca_Bomarea pardina
## 3 Species_Detect_Elevation -1.00 Fawn-breasted Brilliant_Fuchsia macros…
## 4 Species_Detect_Elevation -1.00 Gorgeted Sunangel_Palicourea lineata
## 5 Traits -1.00 Collared Inca_Bomarea pardina
## 6 Traits -1.00 Fawn-breasted Brilliant_Fuchsia macros…
## 7 Traits_Detect -0.995 Collared Inca_Bomarea pardina
## 8 Traits_Detect -0.995 Fawn-breasted Brilliant_Fuchsia macros…
## 9 Traits -0.985 Wedge-billed Hummingbird_Heliconia bur…
## 10 Traits -0.975 Collared Inca_Bomarea multiflora
## # ... with 15 more rows